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- W1987237057 abstract "Although integrable Hamiltonian systems are non-generic (Robinson (13)) they have some importance in classical mechanics, e.g. the two-body problem, a free rigid body not subject to a gravitational field, the Toda lattice (Moser(12)). Arnol'd (cf. (2) and (1), appendix 26) proved that under quite general conditions action-angle coordinates can be introduced. Accordingly we consider a fixed system with n degrees of freedom in the standard form where H 0 is a smooth function of the action variables L i only and I ∈ I and I is an open set of n -tuples of positive reals. now subjected to a periodic impressed force, the resulting system, , being determined by a small, periodic perturbation of the energy function where e is a small positive real and K ( c , I ; α 0 , α 1 , …, a n ) is a smooth function of parameters c ranging over a smooth r -manifold E, I ∈ I , and K has period 2π in each of the angles α i , i.e. (α 0 , …, α n ) ∈ T n ( n -torus). The purpose of this paper is to define the forms of bifurcation of oscillations of the perturbed system ( K ):" @default.
- W1987237057 created "2016-06-24" @default.
- W1987237057 creator A5089064775 @default.
- W1987237057 date "1979-01-01" @default.
- W1987237057 modified "2023-09-27" @default.
- W1987237057 title "Generic bifurcations of forced oscillations of integrable mechanical systems" @default.
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- W1987237057 doi "https://doi.org/10.1017/s0305004100055560" @default.
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